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We discover the unique, simple Lie Algebra of the Third Kind, or LATKe, thatstems from codimension 6 orbifold singularities and gives rise to a kind ofYang-Mills theory which simultaneously is pure and contains matter. The rootspace of the LATKe is 1-dimensional and its Dynkin diagram consists of onepoint. The uniqueness of the LATKe is a vacuum selection mechanism.

Orbifold Singularities, Lie Algebras of the Third Kind (LATKes), and Pure Yang-Mills with Matter